Problem: Divide. Write the quotient in lowest terms. $1\dfrac{1}{4} \div 1\dfrac25 = $
First, let's rewrite $1\dfrac14$ and $1\dfrac25$ as fractions: $1\dfrac{1}{4} \div 1\dfrac25 =\dfrac{5}4 \div \dfrac75$ [How do we write a mixed number as a fraction?] Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac75$ is $\dfrac57$. Now, we can rewrite our expression as a multiplication problem: $\dfrac{5}4 \div \dfrac75=\dfrac54\times\dfrac57$ $=\dfrac{5 \times 5}{4 \times 7}$ $=\dfrac{25}{28}$